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Developing a suitable Deep Neural Network (DNN) often requires significant iteration, where different model versions are evaluated and compared. While metrics such as accuracy are a powerful means to succinctly describe a model's…
Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Time series analysis of fMRI data is an important area of medical statistics for neuroimaging data. The neuroimaging community has embraced mean-field variational Bayes (VB) approximations, which are implemented in Statistical Parametric…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
Multi-modal MRIs are widely used in neuroimaging applications since different MR sequences provide complementary information about brain structures. Recent works have suggested that multi-modal deep learning analysis can benefit from…
Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over…
The notion of a Brain-Computer Interface system is the acquisition of signals from the brain, processing them, and translating them into commands. The study concentrated on a specific sort of brain signal known as Motor Imagery EEG signals,…
A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…
The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known…
Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a diffcult task due to different types of brain abnormalities. Using information and features from multimodal MRI including T1, T1-weighted inversion recovery…
Given a pair of multivariate time-series data of the same length and dimensions, an approach is proposed to select variables and time intervals where the two series are significantly different. In applications where one time series is an…
Deep learning approaches to the segmentation of magnetic resonance images have shown significant promise in automating the quantitative analysis of brain images. However, a continuing challenge has been its sensitivity to the variability of…
Multi-modality image fusion and segmentation play a vital role in autonomous driving and robotic operation. Early efforts focus on boosting the performance for only one task, \emph{e.g.,} fusion or segmentation, making it hard to…
We provide the asymptotic distribution of the major indexes used in the statistical literature to quantify disparate treatment in machine learning. We aim at promoting the use of confidence intervals when testing the so-called group…
Machine learning (ML) has employed various discretization methods to partition numerical attributes into intervals. However, an effective discretization technique remains elusive in many ML applications, such as association rule mining.…
In this paper we study the mean values of some multiplicative functions connected with the divisor function on the short interval of summation. The asymptocic values for such mean values are proved.
Recent years have experienced increasing utilization of complex machine learning models across multiple sources of data to inform more generalizable decision-making. However, distribution shifts across data sources and privacy concerns…